Multiply the following complex numbers, marked as blue dots on the graph: $[3(\cos(\frac{1}{2}\pi) + i \sin(\frac{1}{2}\pi))] \cdot [\cos(\pi) + i \sin(\pi)]$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3(\cos(\frac{1}{2}\pi) + i \sin(\frac{1}{2}\pi))$ ) has angle $\frac{1}{2}\pi$ and radius $3$ The second number ( $\cos(\pi) + i \sin(\pi)$ ) has angle $\pi$ and radius $1$ The radius of the result will be $3 \cdot 1$ , which is $3$ The angle of the result is $\frac{1}{2}\pi + \pi = \frac{3}{2}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{3}{2}\pi$.